American Journal of Computational Linguistics COMPUTATION OF A SUBCLASS OF INFERENCES: PRESUPPOSITION AND ENTAILMENT p,RAVIND K. JOSHI AND RALPH WEISCHEDEL Department of C~~ and I~iar;l"onScience Moore School of Electrical Engineerihg University of Pennsylvania, Philadelphia 19104 This work was partially supported by NSF Grant SOC 72-0546A01 and MC 76-19466. Weischedel was associated with the University of California, Irvine, during the preparation of this manuscript. His present address is Department of Computer Scidnce, University of Delaware, Newark. Copyrlght el977 Association for Computational Linguistics The term "inference1' has been used in many ways. In recent artificial intelligence literature dealing with computational linguistics, it has been used to ref= to any conjecture given a set of facts. The conjecture my be -true or false. In -this sense, "inferencet' includes mre than formally deduced statements. This paper considers a subclass of inferences, known as presupposition and entailment. We exhibit many of their pmperties. In particular, we demanstrate how to compute them by structural means (e.g. -tree transforma- tions). Fwther, we disc~stheir computational properties and their mle in the semantics of natural language. A sentence S entails a sentence S1 if in every context in which S is true, St must also be true. A sentence S presupposes a sentence S" if both S itself entails St' and the (intermal) negation of S also entails S". The system we ha* described computes this subclass of inferences while parsing a sentence. It uses the augnated transition network (ATN). While parsing a sentence, the Am graph retrieves the tree tr,ansformations from the lexicon for any words in the sentence, and applies the tree sfo or mat ion to the appropriate portion of the semaritic representation of the sentence, to obtain entailments and presuppositions. Ftrther, when a specific syntactic cons-truct having a presupposition is pamed, the Pfl3 generates the corresponding presupposition using tree -formations. That presuppsition and entailment are inferences is obvious. However, the requirement in their definition that they be independent of the situation (all context not represented structurally) is stmng. Hence, it is clear that presupposition and entailment are s-trictly a subclass of inferences. As one would hope in studying a res-tricted class of a more geneml phenomenon, this subclass of inferences e~bitsseveral computa- tional and linguistic aspects not exhibited by the geneml class of inferences. Some of these are 1) presupposition and entailment seem to be tied to the definitional (semantic) st~ucturead syntactic structure of language, 2) presupposition and entailment e&ibit complex interaction of semantics and syntax; they exhibit necessary, but not sufficient, semantics of individual words and syntactic constructs, and 3) forthe case of presuppositibn and entailment,there is a na-1 solution to the problem of knowing when to stop drawing inference&, which is an importan-tr problem in inferencing, in genm. The term "inference" has been used in many ways. In recent artificial intelligence litemtire dealing with cqutational linguistics, it has been used to refer to any conjecture given a context (for instance, the context developed from previous text). The conjecture my be true or false. k this sense, "inference" includes mom than formally deduced statements. Further, alternatives to formal deduction procedures are so@t for computing inferences because formal deductive procedures tend to undergo ccmbinatori;ll expLosion . A subclass of inferences that we have studied are presupposition and entailment (defined in Section 1). As one would hope in studying a z-estricted class of a more general phenomenon, this subclass of inferences exhibits several computational and linguistic aspects not eXhibited by the gend class of inferences. One aspect is that presupposition and entailment seem to be tied to the definitional (semantic) structure and syntactic structure of language. As a consequence, we demonstrate how they may be computed by structural means (e. g. tree transfomtions) using &I augmented transition network. A second aspect is that presupposition and entailment exhibit complex interaction of semantics and syntax. They exhibit necessary, but not sufficient, semantics of individual words and of syntactic constructs. Another aspect relates to the problem of lawwing when to stop drawing inferences. There is a natwal solution to this problem far the case of presupposition and entailment . The definitions of presupposition and entailmnt appear in Section 1, with exmqles in Sections 2 and 3. A brief desoription of the system that -5- ccmputes the presuppositions land en-taiIme1a-t~of an input sentence appears in Section 4. (The details of the camgutation and me system are in Weischedel (1976). Detailed comparison of this subclass of inferences with the genawl class of inferences is presented in Section 5. Conclusions are stated in Section 6. An appendix contains sample input--output sessions. In this section, we define the inferences we are interested in[ pm- supposition and entailment), and carment on our use of the tm "pwtics" 2nd wcontext". In order to specify the sub-classes of inferences we are studying, we need same preliminary assumptions and definitions. Inferences, in general., must be made given a particular body of p~grraticinformtion and with respect to texts. Sbce sentences are the simplest cases of texts, we are concentrating on them. Presuppositions and entailments are particularly useful inferences for studying texts havkg sentences containing anbedded sentences, and they may be studied to a limited extent independent of prap&ic jnformatian. 1.1 Subformula-derived We assume that the primary goal of the syntactic cornpnent of a natural language system is to translate Awn natural language sentences to meaning representations selected in an artificial language. Assume further, that the meaning representations selected for Ihglish sentences have a syntax which may be appmximated by a context-free pm. By "approximated1', we mean that there is a context-free &ramm of the semantic representations, though the language given by the g~mrarmay include sane strings which have no interpretation. (For instance, the syntax of ALGOL is often appmxhted by a Backus-Naur form specification. Since we have assumed a context-free syntax for the semantic representations, we may speak of the semantic representations as well-formed fcmulas and as having well-farmed subfmnulas and tree representations. As long as the assumption of context-free syntax for semantic representations is satisfied, the same algorithms and data structures of our system can be used regardless of choice of semantic primitives or type of semantic representation. Let S and Sf be sentences with meaning representations L and Lr respectively. If there is a well-formed subforuila P of L and sane tree trwmformation F such that Lf = F(P), then we say St may be subformula-derived hS. The type of -tree transfornations that are acceptable for F have been formalized and studied extensively in ccmnputat ional linguistics as f inite-state tree transformat ions. The main point of this work is that the presuppositions and entailments of a sentence may be subfomula-derived. We have built a system by which we my specify subformulas P and tree tmnsformations F. The system then automitically generates presuppositions and entaihmts from an input sentence S. 1.2 Fmgmt ics and Context We use context to refer to the situation in which a sentence my occur. Thus, it would include all discourse prior to the sentence under consideration, beliefs of the interpreter, i. e. , in shwt the -state of the intqreter. We use pmtics to describe bll phenomena (and computations mdelling them) that reflect the effect of context. 1.3 Ehtai3men-t A sentence S entails a sentence St if and onlv if in everv context which S is me, St is also true. We may say then that St is an entaibmt of S. This definition is used within linguistics -8r as a test rather than as a rule in a foml system. One discovers apirically whether St is an entailment of S by trying to construct a context in which S is true, but in which St is false. Entailment is not the same as material implication. For instance, let S by "John managed to kiss Mary,' which entails sentence Sf, "John kissed Mary. l1 Givon (1973) argues that even if N ST is true, we would not want to say that 'Wohn did not mage to kiss Mary. l1 The reason is that "managerfseems to presume an attempt. Hence, if John did not kiss Mary, we cannot conclude that John did not manage to kiss Mary, for he may not have attempted to kiss Mary. Though S entails S ' , it is not the case that S St, since that would require NS'SNS. We have shuwn that entailments may be subfda-der~ved,that is, that they may be computed by structural means. As an example, consider the sentence S below; one could represent its rrreaning representatbn as L. S entails Sf, with meaning representation Lf. S. John forced us to leave. L. (IN-m-PAST (force John (EVENT ( IN-THE-PAST (leave we ) ) ) 11 Sf, We left. Lf. (IN=-PAST (leave we)) From the meaning representation selected it is easy to see the appropriate subfdand the identity tree transformtio~which demonstrate that this is a subformula-derived entailment. (This is, of course, a trivial tree .h.ansformation. A nontrivial example appears in Section 1.4, for pnsupposition. ) Many ewmples of entailment axe given in Secticn 2. Notice that it is questionakde whether one understands sentence S or the word Ivforce" if he des not knaw that St is true whenever S is. In this sense, entailment is certainly necessary knowledge ( though not sufficient) for understan- natural*language. We will see this again for presupposition. A second, related concept is the not ion of presupposition.